A fractional-order Maxwell model for non-Newtonian fluids

• DOI: 10.1016/j.physa.2017.04.085
• Publication Date: 2017-04-26T17:30:21Z
• Authors: Y. Carrera; G. Avila-de la Rosa; E.J. Vernon-Carter; J. Alvarez-Ramirez
• Keywords: Harmonic

Abstract This work considers an extension of the fractional-order Maxwell arrangement to incorporate a relaxation process with non-Newtonian viscosity behavior. The resulting model becomes a fractional-order nonlinear differential equation with stable solution converging asymptotically to a unique equilibrium point. Expressions for the corresponding storage and loss moduli as function of strain frequency and amplitude are computed via a first-harmonic analysis of the differential equation. Some distinctive features and their relationship to the classical and fractional-order linear Maxwell models are discussed. Three examples are used to illustrate the ability of the fractional-order Maxwell model to describe experimental data.